Both
issues have been reported.
The workaround for the first issue (picking PDF/Word, etc.) is simply to uncheck the "keep aspect ratio" (or something like that), then provide 0 for both width and hight (or any arbitrary number).

Yes, I know the workardounds, I already solved them both via javascript. I didn't know they were both reported (although, now that I looked at it, I was the one reporting the other issue) so I just wanted to point that out.

I have this same feature request and have discovered the same workarounds. I will vote for the issues.

One thing is vexing me though, when you try and save a mediapicker field that's not an image and you don't apply the workaround you get "The Width field is required." The object model
is flagging that as a required field, which at first seems to be standard MVC attribute based stuff. Only, I can't find the attribute. I've looked at the field model, I've looked at lots of other code and even database settings. I can't find it.

Somehow, somewhere, there is data telling the validator these are required fields. Does anyone know where this is?